Spin-polarized $\beta$-stable neutron star matter: the nuclear symmetry energy and GW170817 constraint

TL;DR

This paper investigates how spin polarization affects the equation of state of neutron star matter, influencing nuclear symmetry energy, cooling processes, and compatibility with GW170817 constraints, suggesting a significant fraction of baryons may be spin-polarized in neutron stars.

Contribution

It introduces a nonrelativistic Hartree-Fock approach with a realistic interaction to study spin-polarized neutron star matter and links the results to gravitational wave observations.

Findings

Nuclear symmetry energy increases with spin polarization.

Up to 60% of baryons in neutron stars may be spin-polarized.

Spin polarization impacts neutron star radius and cooling processes.

Abstract

Magnetic field of rotating pulsar might be so strong that the equation of state (EOS) of neutron star (NS) matter is significantly affected by the spin polarization of baryons. In the present work, the EOS of the spin-polarized nuclear matter is investigated in the nonrelativistic Hartree-Fock formalism, using a realistic density dependent nucleon-nucleon interaction with its spin and spin-isospin dependence accurately adjusted to the Brueckner-Hartree-Fock results for the spin-polarized nuclear matter. The nuclear symmetry energy and proton fraction are found to increase significantly with the increasing spin polarization of baryons, leading to a larger probability of the direct Urca process in the cooling of magnetar. The EOS of the $\beta$-stable np$e\mu$ matter obtained at different spin polarizations of baryons is used as the input for the Tolman-Oppenheimer-Volkov equations to determine the hydrostatic configuration of NS. Based on the GW170817 constraint on the radius $R_{1.4}$ of NS with $M\approx 1.4_\odot$, our mean-field results show that up to $60~\%$ of baryons in the NS merger might be spin-polarized. This result supports the magnetar origin of the blue kilonova ejecta of GW170817 suggested by Metzger et al., and the spin polarization of baryons needs, therefore, to be properly treated in the many-body calculation of the EOS of NS matter before comparing the calculated NS mass and radius with those constrained by the multi-messenger GW170817 observation.